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研究生： 陳昆旻
Chen, Kun-Min
論文名稱： SOFR期貨及期貨選擇權的定價與實證分析：Hull-White雙因子模型與單因子模型比較
Pricing and Empirical Analysis of SOFR Futures and Futures Options: Hull-White Two-Factor vs. One-Factor Models
指導教授： 林士貴
Lin, Shih-Kuei
口試委員: 羅秉政
Kendro Vincent
詹芳書
Chan, Fang-Shu
謝長杰
Hsieh, Chang-Chieh
學位類別： 碩士
Master
系所名稱： 商學院 - 金融學系
Department of Money and Banking
論文出版年： 2024
畢業學年度： 112
語文別： 英文
論文頁數： 59
中文關鍵詞： SOFR 期貨 、SOFR 期貨選擇權 、Hull-White 雙因子模型
外文關鍵詞： SOFR futures, SOFR futures options, Hull-White two-factor model
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    • 自2017年美國替代參考利率委員會(ARRC)推薦SOFR作為美元LIBOR的替代利率以來，持續努力發展SOFR衍生性商品市場。如今，CME的SOFR期貨和期貨選擇權已成為SOFR市場上流動性最好的商品之一。本研究擴展了廣泛使用的Hull-White模型，評估了單因子和雙因子模型對SOFR期貨（線性產品）和期貨選擇權（非線性產品）定價的適用性和表現。在SOFR期貨的實證分析中，我們運用了如RMSRE、RMSE、AIC及BIC等衡量指標，並結合校準誤差來評估兩種模型。結果發現，單因子模型足以適應SOFR期貨市場的需求。對於期貨選擇權，我們最初通過蒙地卡羅模擬驗證了本文推導的（半）解析定價公式。隨後進行模型參數對波動度期限結構的敏感度分析，讓我們進一步了解不同參數對SOFR期貨選擇權波動度的影響。最後，我們發現雙因子模型在常數參數下，相較於單因子模型，更有效地捕捉了SOFR期貨選擇權的波動度期限結構。

    Since the ARRC recommended SOFR as the alternative reference rate to USD LIBOR in 2017, efforts have been made to develop the SOFR derivatives market. Today, CME's SOFR futures and options are among the most liquid in the SOFR market. This study extends the widely used Hull-White model to assess both one-factor and two-factor models for pricing SOFR futures (linear products) and futures options (non-linear products). In our empirical analysis of SOFR futures, we utilized metrics such as RMSRE, RMSE, AIC, and BIC, alongside calibration errors, to evaluate the two models. The one-factor model proved adequate for the SOFR futures market. For SOFR futures options, we initially validated the (semi-)analytical pricing formulas through Monte Carlo simulation. We then conducted a sensitivity analysis of model parameters on the volatility term structure, further understanding their impact on SOFR futures options volatility. Lastly, we found that the two-factor model with constant parameters, more effectively captures the volatility term structure of SOFR futures options compared to the one-factor model.

    摘要 i
    Abstract ii
    Contents iii
    List of Figures v
    List of Tables vi
    1 Introduction 1
    1.1 Background and Motivation 1
    1.2 Research Purpose 6
    2 Literature Review 9
    2.1 Short Rate Models 9
    2.2 The Pricing of SOFR Derivatives 10
    2.3 Empirical Studies on SOFR Futures Options 10
    3 Methodologies 12
    3.1 Hull-White Two-Factor Model 12
    3.1.1 Two-Additive-Factor Gaussian Form 12
    3.1.2 The Pricing of Zero-Coupon Bond 13
    3.1.3 T-Forward Measure 14
    3.1.4 Classical Hull-White Two-Factor Form 15
    3.2 The Pricing of SOFR Futures 17
    3.2.1 One-Month SOFR Futures 17
    3.2.2 Three-Month SOFR Futures 18
    3.3 The Pricing of SOFR Futures Options 19
    3.3.1 One-Month SOFR Futures Options 20
    3.3.2 Three-Month SOFR Futures Options 21
    4 Empirical Results 23
    4.1 Data Description 23
    4.2 Calibration Procedure 25
    4.3 SOFR Futures 28
    4.4 SOFR Futures Options 34
    4.4.1 (Semi-)Analytical and Monte Carlo Methods 34
    4.4.2 Volatility Term Structure: Sensitivity Analysis 37
    4.4.3 Volatility Term Structure: One-Factor vs. Two-Factor Models 39
    5 Conclusions and Future Works 42
    5.1 Conclusions 42
    5.2 Future Works 43
    References 44
    Appendices 47

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